Time average optimization of cycle process with profit and effort discounts

We prove the existence of solution in the problem of time averaged optimization of cyclic processes with both profit and effort discounts and find the respective necessary optimality condition. It is shown that optimal strategy could be selected piecewise continuous if a differentiable profit density has a finite number of critical points. In such a case the optimal motion uses only maximum and minimum velocities as in Arnold's case without any discount

Existence of Self-sustained Oscillations in an Ocean Circulation Box Model with Turbulent Fluxes

Box-models are important for qualitative description of thermohaline circulation. Their bifurcation analysis helps to understand possible mechanisms for the loss of stability. So far, bifurcations in box-models have been studied numerically, except for the saddle-node bifurcation in the Stommel type models. We consider a box-model with turbulent fluxes. We prove that a rapid growth of the transfer function can lead to existence of a limit cycle. This limit cycle collapses to a steady state as the transfer function approaches the step function

Generic Phase Transition and Profit Singularities in Arnold's Model

For one parametric smooth family of pairs of control systems and profit densities on the circle, the transition between optimal strategies of cyclic and stationary types in the problem of maximization of infinite horizon averaged profit is studied. We show that only two types of such transition can be observed for a generic pair, study the corresponding singularities of the averaged profit as a function of the family parameter and prove their stability to small perturbations of such a family. We also complete the classification of generic singularities of the maximum averaged profit for such families

Reduction theorem and normal forms of linear second order mixed type PDE families in the plane

Normal forms for smooth deformation of germ of characteristic equation of second order partial differential equation being linear with respect to second derivative is found near a point of tangency of characteristic direction with the type change line, when this singular point is nondegenerate and non-resonance

Optimization of the Spatial Distribution of Pollution Emission in Water Bodies

The environmental protection of water bodies in Europe is based on the Water Framework Directive, which combines the so called Emission Limits Value and the Water Quality Objective (QO) approaches. The first one sets limits to particular type of emissions, for example the Nitrate Directive, while the second establishes Quality Standards for Biological, Chemical and Hydromorphological Quality Elements, in order to ensure the functioning of freshwater and marine ecosystem and the sustainable use of water bodies. To this regard, mathematical models are valuable tools for reconciliating these approaches, since they allow one to establish a causal link between emission levels and the Quality Standards ("direct problem") and vice-versa ("inverse problem"). In general, Quality Elements are variables or proper combination of variables which define the "status" of a water body. For example, the "chemical status" can be defined by a set of concentrations of chemicals which are potentially harmful for the ecosystem and humans, or the biological status may be based on Quality Elements which include the density of phytoplankton, the presence/absence of Submerged Aquatic Vegetation, the presence/absence of sensitive species etc. In many instances, the Quality Standards can then be expressed as threshold values, below or above which the functioning of the ecosystem is compromised and/or the risk for human health is not acceptable. If this is the case, management policies should be aimed at improving the state of the system and meet those Standards in the near future. In order to be carried in a cost-effective manner, such interventions should be based on a quantitative understanding of the relationships between the Pressures on the system and its State. This task could be very complex in large water bodies, where transport processes play a major role in creating marked gradients and pollution sources may be spatially distributed and/or not well identified. From the scientific point of view, the problem can be stated as follows: a mathematical model should enable one to "map" the spatial distribution of inputs (emissions) into the spatial distribution of the requested output, namely the "indicator" or "metric", which is subjected to a given constraint, the Quality Standard (QS), within the computational dominion. Such analysis may reveal that the QS are not respected only in a given fraction of the water body and, in the most favorable circumstances, identify the pollution sources which cause the problem. In such a case, a selective intervention, aimed at lowering the emission levels of those sources, would probably be more cost effective than the general reduction of the emission levels in the whole area. The spatial distribution of emission sources may also affect the pollution level and, in some instances, a proper redistribution of those sources in a given area, which leaves unchanged the total load, could have positive effect on the pollution level. In this paper, we are going to investigate the above problems in the simplest possible setting, in order to provide a clear interpretation of the results in relation to the most relevant parameters. The paper is organized as follows: in the "methods" section, we present the basic equations and provide insights for solving the problem in the general case as well as in the specific one here presented. The analytical solutions are presented and discussed in the next two sessions and some concluding remarks are then summarized in the conclusive section

Basic Principles of Betavoltaic Elements and Prospects of their Development

The basic technical principles and means of increase in betavoltaitic elements effectiveness have been analyzed by comparing with their closest analogue – photoelectric semiconductor converters. The geometric parameters of radiation sources for these elements and their capacities have been estimated. It is shown the radiation source 63Ni foil thickness should not exceed a few micrometers, and maximum energy conversion efficiency can achieve ~ 16 %

Optimization of stationary solution of a model of size-structured population exploitation

We establish the global stability of a nontrivial stationary state of the size-structured population dynamics in the case where the growth rate, mortality, and exploitation intensity depend only on the size and certain conditions on the model parameters are imposed. We show that a stationary state maximizing the profit functional of population exploitation, exists and is unique. We also obtain a necessary optimality condition, owing to which this state can be found numerically

New features of collective motion of intrinsic degrees of freedom. Toward a possible way to classify the intrinsic states

Three exactly solvable Hamiltonians of complex structure are studied in the framework of a semi-classical approach. The quantized trajectories for intrinsic coordinates correspond to energies which may be classified in collective bands. For two of the chosen Hamiltonians the symmetry SU2xSU2 is the appropriate one to classify the eigenvalues in the laboratory frame. Connections of results presented here with the molecular spectrum and Moszkowski model are pointed out. The present approach suggests that the intrinsic states, which in standard formalisms are heading rotational bands, are forming themselves "rotational" bands, the rotations being performed in a fictious boson space.Comment: 33 pages, 9 figure

Bicategories for boundary conditions and for surface defects in 3-d TFT

We analyze topological boundary conditions and topological surface defects in three-dimensional topological field theories of Reshetikhin-Turaev type based on arbitrary modular tensor categories. Boundary conditions are described by central functors that lift to trivializations in the Witt group of modular tensor categories. The bicategory of boundary conditions can be described through the bicategory of module categories over any such trivialization. A similar description is obtained for topological surface defects. Using string diagrams for bicategories we also establish a precise relation between special symmetric Frobenius algebras and Wilson lines involving special defects. We compare our results with previous work of Kapustin-Saulina and of Kitaev-Kong on boundary conditions and surface defects in abelian Chern-Simons theories and in Turaev-Viro type TFTs, respectively.Comment: 34 pages, some figures. v2: references added. v3: typos corrected and biliography update